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EXAMPLES. 1. Reduce 5s. 4d. 3q. to the decimal of a pounda
Note. In dividing, cyphers may be annexed to the dividends, and the quotients carried to as many places as are necessary ; or they may be supposed to be anRexed, as in this example. 2. Reduce 168. 8d. to the decimal of a pound.
Answer, ,833&c. 3. Reduce 3oz. 17pwts. 3gr. to the decimal of a pound troy.
5. Reduce 2Cwt. 3qr. 21/b. to the decimal of a Ton.
Answer, ,146875. 5. Reduce 16min. 13sec. to the decimal of a day.
Answer, ,01126157 &c. 6. Reduce 15 rods, 10ft. to the decimal of a mile.
Answer, ,04877. 7. Reduce 2 roods, 35 rods, to the decimal of an acre.
Case 3. To find the value of any decimal in the known parts of the integer.
RULE. 1. Multiply the given decimal by so many of the next inferior denomination, as make one of that of which the decimal is a part ; and cut off so many places in the product, as there are places in the decimal ; then the figures at the left hand are whole numbers.
2. Multiply the right hand figures by the parts in the next less denomination, and point off as many figures as before ; proceed in the same manner through all the denominations of the integer, and the left hand figures will be the answer.
EXAMPLES. 1. Required the value of ,653125 of a pound.
31000000 Answer, 13s. Od. 39. 2. What is the value of ,957 of a pound troy ?
10|320 Answer, 11oz. 9pwk. 1687,
What is the value of ,015375 of a Ton?
Answer, 1qr. 6lb. 702. What is the value of ,09955 of a month ?
Ansiver, 2da. 18h. 54m. What is the value of ,387 of a yard ?
Answer, 1gr. 2na.
FEDERAL MONEY. The Federal Currency proceeds in a ten-fold proportion, each superior denomination being ten times the value of that immediately below it ; therefore, as this is the common property of wholé numbers, or chimals, any number of dollars, dimes, cents, and mills, is expressed by dollars and decimal parts of a dellör: Thus, 4 dollars and 7 dimes are 4 dollars and of a dollar, expressed thus, 4,70 dollars. 24 dol. 1 d. 5 c. are 24 dol. and too of a dollar, expressed thus, 24,15 do'. 46 do'. 4 C. 2 in. are 46 dol. and 1 io of a dollar, expressed thus, 46,042 dol. &c. Hence it is plain, that the Federal Money is set down in the same form, and consequently managed in the same manner, in all respects, as decimals.
The first figure at the left hand of the separating point is dollars, and all the rest are eagles ; but in common reckoning, the eagles and dollars are reckoned together ; thus, 51 eagles and 7 dollars are 517 dollars.
Also, dimes and cents are commonly taken tofether, and called cents ; thus, 5 dimes, 2 cents, and 7 mills, are 52 cents and 7 mills. Addition of Federal Money.
RULE. 1.“ Place dollars under dollars, dimes under Cincs, &c.
2. Add them together, as in whole numbers, and point off so many figures at the right hand, for dimes, cents, and mills, as are figures cut off in any of the given numbers.
5. Add 27 eagles, 3 dollars, 4 dimes, 6 cents, 2 mills ; 2 dollars, 36 cents, 8 mills ; 3 cents, 5 mills; 4860 dollars; and 12 dollars, 98 cents, together...
Subtraction of Federal Money.
RULE. Place the figures in the less number under those of the same value in the greater ; then subtract as in whole numbers, and point off the figures, for decimals or dimes, cents, and mills, as in addition.
D. d.c. From 7632,364 167,812 687,8 Take 2975,847 95,946 409,48 Rem. 4656,517
71,866 278,32 4. From 27864 dollars, 28 cents, 4 mills, take 3945 dollars, 84 cents, 9 mills.
Doll. d cm, 27864,284 3945,849
$: From 48 dollars, 20 cents, take 35 dollars, 39
cents, 4 mills.
Multiplication of Federal Money.
RULE. 1. Multiply the numbers, as if they were whole numbers : then point off so many figures at the right hand of the product, for decimals, as are figures pointed off in both numbers,